Variance of binomial vs. hypergeometric

Given \(N\) balls of which \(r\) of them are red and the rest are green. Denote \(X\) as the number of red balls drawn when sampling with replacement and \(Y\) as the number of red balls drawn when sampling without replacement.

  1. What is the difference between the variance of \(X\) and the variance of \(Y\) ?
  2. For what values of \(N,n,r\) is the variance the largest ?

 

 

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